The three-dimensional excitation equations for the longitudinal-irregular circular waveguides with finite conductions of the walls by electron beams in completed form for self-consistent models of gyrotrons, peniotrons, relativistic TWT and BWO had been derived. The possibilities of improving the efficiency of millimeter-wave gyrotron with multimode interaction fields of whispering gallery waves and a relativistic helical electron beam were consider. It is shown that two-mode gyrotron, compared with single-mode allows you to raise the efficiency from 40 to 45%.
